scholarly journals A Comparison of Benson’s Outer Approximation Algorithm with an Extended Version of Multiobjective Simplex Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Paschal B. Nyiam ◽  
Abdellah Salhi
Keyword(s):  
Extreme Points ◽  
Simplex Algorithm ◽  
Outer Approximation ◽  
Efficient Solutions ◽  
Multiple Objective ◽  
Decision Variable ◽  
Multiple Objective Linear Programming ◽  
Extended Version ◽  
Outer Approximation Algorithm ◽  
Nondominated Points

The multiple objective simplex algorithm and its variants work in the decision variable space to find the set of all efficient extreme points of multiple objective linear programming (MOLP). Other approaches to the problem find either the entire set of all efficient solutions or a subset of them and also return the corresponding objective values (nondominated points). This paper presents an extension of the multiobjective simplex algorithm (MSA) to generate the set of all nondominated points and no redundant ones. This extended version is compared to Benson’s outer approximation (BOA) algorithm that also computes the set of all nondominated points of the problem. Numerical results on nontrivial MOLP problems show that the total number of nondominated points returned by the extended MSA is the same as that returned by BOA for most of the problems considered.

scholarly journals A comparative study of two key algorithms in multiple objective linear programming

2019 ◽  
Vol 13 ◽  
pp. 174830261987042
Author(s):  
Paschal B Nyiam ◽  
Abdellah Salhi
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Multiple Objective ◽  
Multiple Objective Linear Programming ◽  
Objective Space ◽  
Linear Programming Problems ◽  
Outer Approximation Algorithm ◽  
Parametric Simplex Algorithm ◽  
Problem Instances ◽  
Comparative Results

Multiple objective linear programming problems are solved with a variety of algorithms. While these algorithms vary in philosophy and outlook, most of them fall into two broad categories: those that are decision space-based and those that are objective space-based. This paper reports the outcome of a computational investigation of two key representative algorithms, one of each category, namely the parametric simplex algorithm which is a prominent representative of the former and the primal variant of Bensons Outer-approximation algorithm which is a prominent representative of the latter. The paper includes a procedure to compute the most preferred nondominated point which is an important feature in the implementation of these algorithms and their comparison. Computational and comparative results on problem instances ranging from small to medium and large are provided.

scholarly journals On the simplex, interior-point and objective space approaches to multiobjective linear programming

2021 ◽  
Vol 15 ◽  
pp. 174830262110084
Author(s):  
Paschal B Nyiam ◽  
Abdellah Salhi
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Interior Point Method ◽  
Simplex Algorithm ◽  
Affine Scaling ◽  
Decision Variable ◽  
Multiple Objective Linear Programming ◽  
Objective Space ◽  
Variable Space

Most Multiple Objective Linear Programming (MOLP) algorithms working in the decision variable space, are based on the simplex algorithm or interior-point method of Linear Programming. However, objective space based methods are becoming more and more prominent. This paper investigates three algorithms namely the Extended Multiobjective Simplex Algorithm (EMSA), Arbel’s Affine Scaling Interior-point (ASIMOLP) algorithm and Benson’s objective space Outer Approximation (BOA) algorithm. An extensive review of these algorithms is also included. Numerical results on non-trivial MOLP problems show that EMSA and BOA are at par and superior in terms of the quality of a most preferred nondominated point to ASIMOLP. However, ASIMOLP more than holds its own in terms of computing efficiency.

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